The Jeffersonian Republicans were doomed to split. A one party system, which US politics generally became by 1820, can't last forever in a democratic society. Even before the 1824 election, Republicans disagreed over tariffs, expansion, slavery, and other hot button issues of the day. You had ex-Federalists like Adams, moderates like Clay who took ideas from both Hamilton and Jefferson, the "Tertium Quid" old guard, and then hardline right-wingers like Jackson and Calhoun. A party with that many disagreeing factions can't work for very long and it's actually pretty surprising that the Republicans lasted until 1828.